Download 8 G Angles1617 - Farmington Municipal Schools

8: Q4
Topic Proficiency Scale
Domain: Geometry
Topic: Angles
4.0
Going Beyond
I know all of the Simple and Complex Learning Goals and my understanding goes
beyond the grade level target.
I know all of the Simple and Complex Learning Goals.
3.0
Complex Goals
Grade Level Target
C1: Use informal arguments to establish facts about the angles created when
2.5
I know all of the Simple Learning Goals plus some of the Complex Learning Goals.
parallel lines are cut by a transversal. (8.G.5)
C2: Use informal arguments to establish facts about the angle sum and exterior
angles of triangles and about the Angle-Angle Criterion for similarity of triangles.
(8.G.5)
I know all of the Simple Learning Goals.
2.0
Simple Goals
Academic Vocabulary:
V1: Angle-Angle Criterion (AA Criterion)
V2: exterior angles
V3: interior angles
V4: transversal
S1: Know facts about the angles created when parallel lines are cut by a
transversal.
S2: Know facts about angle sum and exterior angles of triangles and the angleangle criterion for similarity of triangles.
1.5
1
0.5
0
I know all but one of the Simple Learning Goals.
I know some of the Simple Learning Goals.
I know only one of the Simple Learning Goals.
No evidence of knowing the Learning Goals.
©Farmington Municipal Schools - 8th grade NMCCSS Math
Revised May, 2016
8: Q4
Teacher Resources
Geometry (G): Angles Understand congruence and similarity using physical models, transparencies, or geometry software.
Standards
Mathema,cal Agile Mind
Explana,ons and Examples
Students are Prac,ces
expected to:
8.G.A.5. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-­‐
angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. Connec=ons: 6-­‐8.WHST.2b,f;
6-­‐8.WHST.1b; ET08-­‐S6C1-­‐03;
ET08-­‐S1C1-­‐01; ET08-­‐S1C3-­‐03
8.MP.3. Construct viable arguments and cri=que the reasoning of others. Topic 14: Exploring Geometric Rela=onships.
Students can informally prove rela=onships with transversals. Example: Show that m! + m!
+ m! = 180˚ if l and m are parallel lines and t1 & t2 are transversals. ! + !
+ !
= 180˚. Angle 1 and Angle 5 are congruent because •
they are corresponding angles (!
8.MP.4. Model with mathema=cs. !
8.MP.6. ACend to precision. Therefore m!
). !
can be subs=tuted for . !
because alternate interior angles are congruent. !
can be subs=tuted for!
+ m!
. + m!
= 180˚ !
Students can informally conclude that the sum of a triangle is 180o (the angle-­‐
sum theorem) by applying their understanding of lines and alternate interior angles. Examples: •
In the figure below, line x is parallel to line yz: !
•
Angle a is 35 o because it alternates with the angle inside the triangle that measures 35 o. Angle c is 80 o because it alternates with the angle inside the triangle that measures 80 o. Because lines have a measure of 180 o, and angles a + b + c form a straight line, then angle b must be 65 o (180 – 35 + 80 = 65). Therefore, the sum of the angles of the triangle are 35 o + 65 o + 80 o.
©Farmington Municipal Schools - 8th grade NMCCSS Math
Revised May, 2016